\documentclass[11pt]{article}
\usepackage{makeidx}
\usepackage{multirow}
\usepackage{multicol}
\usepackage[dvipsnames,svgnames,table]{xcolor}
\usepackage{graphicx}
\usepackage{epstopdf}
\usepackage{ulem}
\usepackage{hyperref}
\usepackage{amsmath}
\usepackage{amssymb}
\author{Michael}
\title{}
\usepackage[paperwidth=612pt,paperheight=792pt,top=56pt,right=42pt,bottom=56pt,left=85pt]{geometry}

\makeatletter
	\newenvironment{indentation}[3]%
	{\par\setlength{\parindent}{#3}
	\setlength{\leftmargin}{#1}       \setlength{\rightmargin}{#2}%
	\advance\linewidth -\leftmargin       \advance\linewidth -\rightmargin%
	\advance\@totalleftmargin\leftmargin  \@setpar{{\@@par}}%
	\parshape 1\@totalleftmargin \linewidth\ignorespaces}{\par}%
\makeatother 

% new LaTeX commands


\begin{document}



\[
\begin{array}{l}
\nabla  \cdot \left( {\begin{array}{*{20}{c}}
a&0\\
0&b
\end{array}} \right)\left( \begin{array}{l}
{u_x}\\
{u_y}
\end{array} \right) = \nabla  \cdot \left( \begin{array}{l}
a{u_x}\\
b{u_y}
\end{array} \right) = {\left( {a{u_x}} \right)_x} + {\left( {b{u_y}}
\right)_y}\\
\nabla  \cdot \left( \begin{array}{l}
{u_r}\\
\frac{1}{r}{u_\theta }
\end{array} \right) = \frac{1}{r}{\left( {r{u_r}} \right)_r} +
\frac{1}{{{r^2}}}{u_{\theta \theta }} = {u_{rr}} + \frac{1}{r}{u_r} +
\frac{1}{{{r^2}}}{u_{\theta \theta }}\\
\nabla  \cdot \left( {\begin{array}{*{20}{c}}
a&0\\
0&b
\end{array}} \right)\left( \begin{array}{l}
{u_r}\\
\frac{1}{r}{u_\theta }
\end{array} \right) = \nabla  \cdot \left( \begin{array}{l}
a{u_r}\\
b\frac{1}{r}{u_\theta }
\end{array} \right) = \frac{1}{r}{\left( {ra{u_r}} \right)_r} +
\frac{1}{{{r^2}}}{\left( {b{u_\theta }} \right)_\theta } = \\
= \frac{1}{r}a{u_r} + {a_r}{u_r} + a{u_{rr}} + \frac{1}{{{r^2}}}\left(
{{b_\theta }{u_\theta } + b{u_{\theta \theta }}} \right)\\
\frac{1}{r}a{u_r} + {a_r}{u_r} + a{u_{rr}} + \frac{1}{{{r^2}}}\left( {{b_\theta
}{u_\theta } + b{u_{\theta \theta }}} \right) - \sigma u = f\\
a{u_{rr}} = f + \sigma u - \frac{1}{r}a{u_r} - {a_r}{u_r} -
\frac{1}{{{r^2}}}\left( {{b_\theta }{u_\theta } + b{u_{\theta \theta }}} \right)
\end{array}
\]



\end{document}